Comparison And Analysis Of Two Kinds Of Reanalysis Mean Monthly Height Fields' Spectral Structures

Against practical problem analyzed by monthly mean hemisperical potential hight field spherical function, it was compared and analyzed that errors from the mode and cross angle calculation of the standardized associated Legendre function (?)_m+2k^m using of common trapeziod, simpson integral formula and the numerical integral expression which WU Xin-yuan finds.The results are given as follow: When m equal to zero and one, the mode and cross angle of (?)_m+2k^m calculation precision using of WU Xin-yuan integral expression is better than that using of the two common integral formulae; when m is not less than two, the precision of trapeziod integral formula is higher than that of WU Xin-yuan integral expression, whose errors from the mode and cross angle calculation is below 10^-4 and 2×10^-3°. Because variance spectrum of monthly mean hemisperical potential hight field spherical function has the basic character of reduced dimensionality and low order, it is able to improve the precision of monthly mean hemisperical potential hight field spherical function by using WU Xin-yuan integral expression as a substitute for the common integral formulae. By using this analysis, comparison and analysis of the spectral space-time structure of the global atmospheric monthly mean geopotential height fields from NCEP-DOE AMIP-Ⅱand ERA-40 reanalysis data sets is performed in this paper. The main results are as follows. 1) The spectral structure of the steady wave (?)^* mainly composed of myriametric wave on the upper level or in the Southern Hemisphere or in winter is simpler than that on the lower level or in the Northern Hemisphere or in summer. 2) The spectral structure of the anomaly fields in the Southern Hemisphere where the structure varied little as season changed is simpler than that in the Northern Hemisphere in which the structure in spring and winter is more complicated than that in winter and summer. The anomaly spectrum is mainly consist of myriametric wave in stratosphere and of long and myriametric wave in troposphere but short wave can not be ignored at tropopause and closed to earth. 3) Because of a lack of correction to the underestimated ground temperature of Antarctica in the N data, there is an obvious spectrum difference of steady wave (?)^* below 700 hPa in the Southern Hemispheric between the N and E data that bellow 700 hPa, the structure of the N data in the Southern Hemisphere is more complex than that in the Northern Hemisphere apparently, which dose not meet the general rule from the first conclusion, and yet the spectrum of the E data have not quite a contrast in the two hemisphere. The lack also result in that on the low level, the spectrum of anomaly fields {H'(t)} in the Southern Hemisphere is simpler than that in the Northern Hemisphere.